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Simple difference quotient question. Function -> simplify answer

  1. Aug 28, 2012 #1
    Simple difference quotient question. Function --> simplify answer

    1. The problem statement, all variables and given/known data

    I just don't understand this question! Here, I will take a picture of it. Can someone please explain how I answer these? Or even show me a website that shows how to do these? Its not in my review book.

    QUESTION is in ATTACHMENTS!

    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Aug 28, 2012 #2

    vela

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    Re: Simple difference quotient question. Function --> simplify answer

    It seems pretty straightforward what the question is asking. What specifically don't you understand?
     
  4. Aug 28, 2012 #3
    Re: Simple difference quotient question. Function --> simplify answer

    Can you tell me the first step? When you look at this, what is the first thing you see/do?
     
  5. Aug 28, 2012 #4

    vela

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    Re: Simple difference quotient question. Function --> simplify answer

    Exactly what the problem statement says: evaluate the difference quotient. If you don't understand what that means, try looking up "difference quotient" in your book.
     
  6. Aug 28, 2012 #5
    Re: Simple difference quotient question. Function --> simplify answer

    Must be missing something here.

    I would plug in the f(x) values to the 2nd function, but there is no x's, just h ? How do I plug in values?
     
  7. Aug 28, 2012 #6

    Mark44

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    Re: Simple difference quotient question. Function --> simplify answer

    The problem is asking you to evaluate the difference quotient to find f'(3).
     
  8. Aug 28, 2012 #7
    Re: Simple difference quotient question. Function --> simplify answer

    wow I'm lost. :(
     
  9. Aug 28, 2012 #8
    Re: Simple difference quotient question. Function --> simplify answer

    Dude, f(x) = f(3+h) if x = 3+h
     
  10. Aug 28, 2012 #9

    Mark44

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    Re: Simple difference quotient question. Function --> simplify answer

    The difference quotient to find the derivative of a function, f'(x), looks like this:

    $$ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$$

    The difference quotient to find the derivative of a function at a specific number a, f'(a), looks like this:

    $$ f'(a) = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}$$

    Do you recognize that your problem is asking for f'(3)?
     
  11. Aug 28, 2012 #10

    SammyS

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    Re: Simple difference quotient question. Function --> simplify answer

    Here's the image:

    attachment.php?attachmentid=50253&d=1346172108.jpg
    ***************************

    So, if [itex]f(x)=4+3x-x^2\,,[/itex] then what is [itex]f(3+h)\ ?[/itex]
     
  12. Aug 28, 2012 #11
    Re: Simple difference quotient question. Function --> simplify answer

    SammyS, that is the one part I am having trouble fully understanding....
     
  13. Aug 28, 2012 #12

    vela

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    Re: Simple difference quotient question. Function --> simplify answer

    It would have helped if you could have said that right from the beginning.

    In f(x)=4+3x-x2, the x is what's called a dummy variable. Anything you put in the lefthand side where the x is shows up wherever the x appears on the righthand side. For example, suppose you have g(x) = 2x+4. Then
    \begin{align*}
    g(y) = 2y+4 \\
    g(h+3) = 2(h+3)+4 \\
    g(4z) = 2(4z)+4 \\
    g(weasel) = 2(weasel)+4 \\
    g(3) = 2(3)+4 = 10
    \end{align*}
    Now tell us what you think f(3+h) is equal to in your problem.
     
  14. Aug 28, 2012 #13

    Mark44

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    Re: Simple difference quotient question. Function --> simplify answer

    Apparently you don't understand how to evaluate a function's formula.

    If g(t) = 3 - t2 (for example)
    then g(1) = 3 - (1)2 = 3 - 1 = 2
    and g(5) = 3 - (5)2 = 3 - 25 = -23
    and g(a + 2) = 3 - (a + 2)2

    So for your function, what is f(3 + h)?
     
  15. Aug 28, 2012 #14
    Re: Simple difference quotient question. Function --> simplify answer

    "So for your function, what is f(3 + h)?"

    f(3+h) = 4 + 3(3+h) - (3+h)^2 ?
     
  16. Aug 28, 2012 #15

    Mark44

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    Re: Simple difference quotient question. Function --> simplify answer

    Yes. You'll need to expand the right side and collect common terms.
     
  17. Aug 28, 2012 #16

    vela

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    Re: Simple difference quotient question. Function --> simplify answer

    Yup, that's it.
     
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